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maxe.jl
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maxe.jl
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# Calculates Emax at terminal period
function maxET(SST::Array, MC_ϵ::Array)
maxE = zeros(size(SST,1),1)
vbar = zeros(size(SST,1),4)
for i = 1:size(SST,1)
state = SST[i]
r1 = mean(exp.(R1(state[1],state[2],state[3],MC_ϵ[1,:])))
r2 = mean(exp.(R2(state[1],state[2],state[3],MC_ϵ[2,:])))
r3 = R3(state[1],state[4],0.0)
r4 = R4(0.0)
maxE[i] = max(r1, r2, r3, r4)
vbar[i,:] = [r1 r2 r3 r4]
end
fmaxE = OrderedDict(zip(SST,maxE))
fEv1 = OrderedDict(zip(SST,vbar[:,1]))
fEv2 = OrderedDict(zip(SST,vbar[:,2]))
fEv3 = OrderedDict(zip(SST,vbar[:,3]))
fEv4 = OrderedDict(zip(SST,vbar[:,4]))
return fmaxE, fEv1, fEv2, fEv3, fEv4
end
# Calculates Emax at t=2,...,T-1
function maxEt(SSt::Array, fEmax::OrderedDict, MC_ϵ::Array)
maxE = zeros(size(SSt,1),1)
vbar = zeros(size(SSt,1),4)
for i = 1:size(SSt,1)
state = SSt[i]
d3 = state + [1,0,0,1-state[4]]
d3[1] = min(20,d3[1])
v1 = mean(exp.(R1(state[1],state[2],state[3],MC_ϵ[1,:])) .+ p.β*fEmax[state+[0,1,0,-state[4]]])
v2 = mean(exp.(R2(state[1],state[2],state[3],MC_ϵ[2,:])) .+ p.β*fEmax[state+[0,0,1,-state[4]]])
if d3[1] < 20
v3 = R3(state[1],state[4],0.0) .+ p.β*fEmax[d3]
else
v3 = R3(state[1],state[4],0.0)
end
v4 = R4(0.0) .+ p.β*fEmax[state+[0,0,0,-state[4]]]
maxE[i] = max(v1, v2, v3, v4)
vbar[i,:] = [v1 v2 v3 v4]
end
fmaxEt = OrderedDict(zip(SSt,maxE))
fEv1 = OrderedDict(zip(SSt,vbar[:,1]))
fEv2 = OrderedDict(zip(SSt,vbar[:,2]))
fEv3 = OrderedDict(zip(SSt,vbar[:,3]))
fEv4 = OrderedDict(zip(SSt,vbar[:,4]))
return fmaxEt, fEv1, fEv2, fEv3, fEv4
end
# Combines both together
function genmaxEAll(Emaxall::OrderedDict,Domain_set::OrderedDict,epsilon::Array)
fmaxE, fEv1, fEv2, fEv3, fEv4 = maxET(T,MC_ϵ)
# Store it in a dictionary with key = t, value = Emax
maxEall = OrderedDict(T => fmaxE)
Ev1all = OrderedDict(T => fEv1)
Ev2all = OrderedDict(T => fEv2)
Ev3all = OrderedDict(T => fEv3)
Ev4all = OrderedDict(T => fEv4)
for t = reverse(2:T-1)
fmaxE, fEv1, fEv2, fEv3, fEv4 = maxEt(Domain_set[t], Emaxall[t+1], MC_ϵ)
tempDict = OrderedDict(t => fmaxE)
tempDict1 = OrderedDict(t => fEv1)
tempDict2 = OrderedDict(t => fEv2)
tempDict3 = OrderedDict(t => fEv3)
tempDict4 = OrderedDict(t => fEv4)
maxEall = merge(maxEall,tempDict)
Ev1all = merge(Ev1all,tempDict1)
Ev2all = merge(Ev2all,tempDict2)
Ev3all = merge(Ev3all,tempDict3)
Ev4all = merge(Ev4all,tempDict4)
println(t)
end
return maxEall, Ev1all, Ev2all, Ev3all, Ev4all
end
# auxiliary functions
function createX(fmaxE::OrderedDict, fEv1::OrderedDict, fEv2::OrderedDict, fEv3::OrderedDict, fEv4::OrderedDict)
n = size(collect(values(fmaxE)),1)
x1 = collect(values(fmaxE)) .- collect(values(fEv1))
x2 = collect(values(fmaxE)) .- collect(values(fEv2))
x4 = collect(values(fmaxE)) .- collect(values(fEv4))
x5 = (collect(values(fmaxE)) .- collect(values(fEv1))).^0.5
x6 = (collect(values(fmaxE)) .- collect(values(fEv2))).^0.5
x7 = (collect(values(fmaxE)) .- collect(values(fEv3))).^0.5
x8 = (collect(values(fmaxE)) .- collect(values(fEv4))).^0.5
if param > 1
x3 = collect(values(fmaxE)) .- collect(values(fEv3))
x = [ones(n,1) x1 x2 x3 x4 x5 x6 x7 x8]
else
x = [ones(n,1) x1 x2 x4 x5 x6 x7 x8]
end
return x
end
function OLS(y,x)
β = (x'*x)^(-1) * (x' * y)
end
function genApproxDataT(Domain::Array, MC_ϵ::Array)
fmaxE, fEv1, fEv2, fEv3, fEv4 = maxET(Domain, MC_ϵ)
fEmax = EmaxT(Domain, MC_ϵ)
y = collect(values(fEmax)) .- collect(values(fmaxE))
x = createX(fmaxE, fEv1, fEv2, fEv3, fEv4)
βap = OLS(y,x)
return βap, fEmax
end
function ApproximateTerminal(ApproxS::Int64, MC_ϵ::Array)
rngDomain = sample(Domain_set[T], ApproxS; replace=false)
βap, fEmaxS = genApproxDataT(rngDomain, MC_ϵ)
fmaxE, fEv1, fEv2, fEv3, fEv4 = maxET(Domain_set[T], MC_ϵ)
fEmax = EmaxT(Domain_set[T], MC_ϵ)
yfull = collect(values(fEmax)) .- collect(values(fmaxE))
xfull = createX(fmaxE, fEv1, fEv2, fEv3, fEv4)
yhat = xfull*βap
for i = 1:size(yhat,1)
if yhat[i] < 0
yhat[i] = 0
end
end
Emaxhat = yhat .+ collect(values(fmaxE))
fEmaxhat = OrderedDict(zip(Domain_set[T], Emaxhat))
fEmaxhat = merge(fEmaxhat, fEmaxS)
Domain = collect(keys(fEmaxhat))
df = DataFrame(Emax = collect(values(fEmax)), maxE = collect(values(fmaxE)), yf = yfull,
Ev1val = collect(values(fEv1)), Ev2val = collect(values(fEv2)), Ev3val = collect(values(fEv3)),
Ev4val = collect(values(fEv4)), yhat = yhat, Emaxhat = Emaxhat, test = Domain)
df |> save("output/T40_$(param)aprox_S$(ApproxS).csv")
return fEmaxhat
#return Emaxhat, fEmaxhat
end
function genApproxData(Domain::Array, MC_ϵ::Array, fEmaxhat::OrderedDict)
fmaxE, fEv1, fEv2, fEv3, fEv4 = maxEt(Domain, fEmaxhat, MC_ϵ)
fEmax = Emaxt(Domain, fEmaxhat, MC_ϵ)
y = collect(values(fEmax)) .- collect(values(fmaxE))
x = createX(fmaxE, fEv1, fEv2, fEv3, fEv4)
βap = OLS(y,x)
return βap, fEmax
end
function ApproximateOnce(ApproxS::Int64, Domain::Array, fEmaxhat::OrderedDict, MC_ϵ::Array)
rngDomain = sample(Domain, ApproxS; replace=false)
βap, fEmaxS = genApproxData(rngDomain, MC_ϵ, fEmaxhat)
fmaxE, fEv1, fEv2, fEv3, fEv4 = maxEt(Domain, fEmaxhat, MC_ϵ)
xfull = createX(fmaxE, fEv1, fEv2, fEv3, fEv4)
yhat = xfull*βap
for i = 1:size(yhat,1)
if yhat[i] < 0
yhat[i] = 0
end
end
Emaxhat = yhat .+ collect(values(fmaxE))
fEmaxhat = OrderedDict(zip(Domain, Emaxhat))
fEmaxhat = merge(fEmaxhat, fEmaxS)
return fEmaxhat
end
function genEmaxAllHat(Domain_set::OrderedDict, ApproxS::Int64)
println("\n Backward induction \n")
println("\n Solving Approximation Model \n")
println("== Iteration t=$T ==\n")
@time fEmaxhat, tEmaxhat= @timed ApproximateTerminal(ApproxS, MC_ϵ[:,:,T])
Emaxallhat = OrderedDict(T => fEmaxhat)
timeEmaxhat = Array{Float64}(undef, T-1, 2)
timeEmaxhat[T-1,:] = [T tEmaxhat]
for t = reverse(2:T-1)
println("== Iteration t=$t ==\n")
if size(Domain_set[t],1) >= ApproxS
@time fEmaxhat, tEmaxhat = @timed ApproximateOnce(ApproxS, Domain_set[t], Emaxallhat[t+1], MC_ϵ[:,:,t])
else
@time fEmaxhat, tEmaxhat = @timed Emaxt(Domain_set[t], Emaxallhat[t+1], MC_ϵ[:,:,t])
end
timeEmaxhat[t,:] = [t tEmaxhat]
tempDict = OrderedDict(t => fEmaxhat)
Emaxallhat = merge(Emaxallhat,tempDict)
end
return Emaxallhat, timeEmaxhat
end